avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?
(1) y = 3
(2) x - y = 3
Target question: What is the value of (x+y)²? Given: x² - y² = 27 Statement 1: y = 3 Take
x² - y² = 27 and replace y with 3 to get: x² - (3)² = 27
Evaluate: x² - 9 = 27
Simplify: x² = 18
So, EITHER x = √18 OR x = -√18
Let's test each case:
Case a: x = √18 and y = 3. So, (x + y)² = (√18 + 3)². So, in this case,
the answer to the target question is (√18 + 3)²Case b: x = -√18 and y = 3. So, (x + y)² = (-√18 + 3)². So, in this case,
the answer to the target question is (-√18 + 3)²NOTE: We need not actually calculate the values of (√18 + 3)² and (-√18 + 3)². We need only see that the two values are DIFFERENT
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x - y = 3 Take
x² - y² = 27 and FACTOR the left side to get: (x + y)(x - y) = 27
Replace (x-y) with 3 to get: (x + y)(3) = 27
So, it must be the case that (x+y) = 9
If (x+y) = 9, then (x+y)² = 81
So,
the answer to the target question is 81Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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